Page 13 - Partition & Adsorption of Organic Contaminants in Environmental Systems

4 IMPORTANT THERMODYNAMIC PROPERTIES

dE = T dS - P dV (1.8)

For any other process, dq π TdS and dw π PdV. However, the difference
between TdS and PdV (i.e., dE) is a state function. Therefore, Eq. (1.8) holds
for all processes, whether or not reversible.
According to the second law of thermodynamics, the criterion for whether
a process is taking place reversibly (i.e., at equilibrium) or spontaneously
within a completely isolated system (i.e., the one at constant volume and inter-
nal energy) is given as

( dS) EV ≥ 0 (1.9)
,
that is, the overall entropy change of the system is zero for an equilibrium
process but increases for a spontaneous process. The fact that (dS) E,V can never
be less than zero is a consequence of the second law.
Chemical processes of most interest usually take place at constant temper-
ature and pressure. A new criterion is therefore required to indicate whether
a process is reversible or spontaneous under this condition. If we now allow
a process to take place initially in an isolated system and then adjust the tem-
perature by reversible absorption (or emission) of heat and adjust the pres-
sure by reversible expansion (or contraction) at constant temperature, the
entropy change from the adjustment will be dq/T = (dE + PdV)/T. The change
in entropy of the system, which is no longer an isolated system, after this
adjustment will be

( dS) TP = ( dS) E V + dE T P dV T (1.10)
+
,
,
Substituting Eq. (1.9) into Eq. (1.10) gives
- (
- ( ) EV = dE P dV TdS ) T P £ 0 (1.11)
+
TdS
,
,
The quantities on both sides will therefore be negative for spontaneous
processes, zero for equilibrium processes, and never positive.
One can express the right side of Eq. (1.11) by defining a new state func-
tion, G, the Gibbs function or Gibbs free energy, as
-
-
G = E + PV TS = H TS (1.12)
At constant temperature and pressure, one gets
( dG) TP = dE P dV T dS (1.13)
-
+
,
From Eqs. (1.11) and (1.13) the condition that
( dG) £ 0 (1.14)
TP
,